Problem: Reduce to lowest terms: $ \dfrac{3}{7} \div - \dfrac{6}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{6}{5}$ is $- \dfrac{5}{6}$ Therefore: $ \dfrac{3}{7} \div - \dfrac{6}{5} = \dfrac{3}{7} \times - \dfrac{5}{6} $ $ \phantom{ \dfrac{3}{7} \times - \dfrac{5}{6}} = \dfrac{3 \times -5}{7 \times 6} $ $ \phantom{ \dfrac{3}{7} \times - \dfrac{5}{6}} = \dfrac{-15}{42} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-15}{42} = \dfrac{-15 \div 3}{42 \div 3} = -\dfrac{5}{14} $